Distribution of particles and fusions in a Fusor
Posted: Fri Sep 18, 2009 4:00 am
Distribution of particles and fusions in a Fusor and implications for the Polywell.
This new topic is prompted by my reinvestigation of a presentation from Univ. of Wisconsin in the link below.
http://iec.neep.wisc.edu/usjapan/6th_US ... miyasu.pdf
and my ruminations about a previous post in another thread.
viewtopic.php?t=1258&start=75
First let me say that my statement in that thread about the average energy of neutrals in a gridded fusor is way off. A virgin/ first generation neutral may start with low energy but after repeated collisions with fast ions or second generation fast neutrals (if not ionized) will gain a lot of energy (speed). If ionized it will become fast, if it then recombines with a free electron(not hitting the wall or grid) it is a second generation neutral with its retained high speed.
My interpretation of the U. W. presentation are:
1) The graphs on page 13 shows the ions concentrating near the center at drive energies above ~ 5-10 KeV, suggesting significant confluence and potential anode formation, despite the presumed dominance of neutrals in this system.
2) The graphs on pages 14,15 show the fusion rates of the various species at various locations in the fusor. They show steady state being reached in a few micro seconds, which supports Dr Bustard's claim that WB6 pulses of ~ 400 micro seconds reflects physics under steady state conditions.
3) While the electron measurements appear sparse (on page 13), the curve in the electron density vs drive voltage suggests to me a parabolic potential well instead of a square potential well that A. Carlson favors. ---Upon further reflection while typing this I realize that this may not be implied, but I left it in so that it can be dissected by others. Also, see earlier graphs in the presentation.
4) The distribution of ion- ion fusions are more concentrated in the center than I would have suspected. I assume this is due to significant confluence (focus) of ion flows with significant retained radial flows over the lifetimes of the ions, which is ~ 100 passes before being lost to structure collisions. I don't know why there is not a small tail extending past the cathode grid. Perhaps it reflects some cutoff sensitivity in their measuring system, or how steep the relationship is between the ion- neutral ratios and the types of fusions.
5) In this gridded fusor design with dominate neutral populations ( I don't know if their experiments included ion guns or not) the ion- neutral and neutral - neutral collisions dominate by a factor of ~100 overall but this starts to reverse as the core is approached.
6). My impression that the ion- neutral fusion collisions were randomly distributed throughout the fusor (as are the neutral- neutral fusions) was wrong. That these ion- neutral fusions increase towards the center until presumably the increasing ion concentrations shift the reaction probability to more favor the ion- ion fusion collisions should(?) relax the requirements for maximizing the ion/ neutral ratios in the Polywell that is required to approach B^4 scaling.
7) The graphs on page 13 show large ion, neutral and electron numbers concentrating near the cathode grid or wall at energies below several hundred electron volts. I'm guessing that this reflects some artifact as opposed to some transitional effect dependant on Debye sheaths, etc. I cannot see neutral distributions being affected by such unless there are significantly increased recombinations in those areas and conditions. Does this have any applications to the arguments about border conditions that Dr. Carlson has put forth in the past?
Keep in mind that the Polywell should maximize the ion/ neutral ratios much more than gridded fusors through both magnetic shielding, which will not only greatly decrease energy losses, but also reduce internal secondary neutral populations by ion neutralizations on internal structures such as the magrid or a material cathode grid. Actually, I don't know what the ratio of recombined neutral populations derived from free electron recombinations vs hitting the cathode or wall is, but the magnetic shielding (and virtual cathode) can only help, perhaps to a significant extent. This should also significantly decrease pollution of the system with sputtered metal ions, etc.
The other (major) advantage of the Polywell is the Wiffleball trapping factor which is claimed to increase internal ion to external ion ratios within the magrids by a factor of ~ 100-1000. Since the neutral density should be ~ equal throughout the vacuum vessel there would be no concentrating effects inside the magrid and thus the ion/ neutral ratios inside the magrids should greatly favor ion- ion fusion collisions over ion- neutral, or fast neutral- neutral collisions ( or ion- target, or neutral- target collisions in a non shielded gridded fusor).
This dominance of ions inside the machine also allows the slow ions near the Wiffleball border to anneal their transverse motions (if you accept that annealing is real) without random motion neutrals interfering.
Any comments, corrections, expansions, laughs or groans?
Dan Tibbets
This new topic is prompted by my reinvestigation of a presentation from Univ. of Wisconsin in the link below.
http://iec.neep.wisc.edu/usjapan/6th_US ... miyasu.pdf
and my ruminations about a previous post in another thread.
viewtopic.php?t=1258&start=75
First let me say that my statement in that thread about the average energy of neutrals in a gridded fusor is way off. A virgin/ first generation neutral may start with low energy but after repeated collisions with fast ions or second generation fast neutrals (if not ionized) will gain a lot of energy (speed). If ionized it will become fast, if it then recombines with a free electron(not hitting the wall or grid) it is a second generation neutral with its retained high speed.
My interpretation of the U. W. presentation are:
1) The graphs on page 13 shows the ions concentrating near the center at drive energies above ~ 5-10 KeV, suggesting significant confluence and potential anode formation, despite the presumed dominance of neutrals in this system.
2) The graphs on pages 14,15 show the fusion rates of the various species at various locations in the fusor. They show steady state being reached in a few micro seconds, which supports Dr Bustard's claim that WB6 pulses of ~ 400 micro seconds reflects physics under steady state conditions.
3) While the electron measurements appear sparse (on page 13), the curve in the electron density vs drive voltage suggests to me a parabolic potential well instead of a square potential well that A. Carlson favors. ---Upon further reflection while typing this I realize that this may not be implied, but I left it in so that it can be dissected by others. Also, see earlier graphs in the presentation.
4) The distribution of ion- ion fusions are more concentrated in the center than I would have suspected. I assume this is due to significant confluence (focus) of ion flows with significant retained radial flows over the lifetimes of the ions, which is ~ 100 passes before being lost to structure collisions. I don't know why there is not a small tail extending past the cathode grid. Perhaps it reflects some cutoff sensitivity in their measuring system, or how steep the relationship is between the ion- neutral ratios and the types of fusions.
5) In this gridded fusor design with dominate neutral populations ( I don't know if their experiments included ion guns or not) the ion- neutral and neutral - neutral collisions dominate by a factor of ~100 overall but this starts to reverse as the core is approached.
6). My impression that the ion- neutral fusion collisions were randomly distributed throughout the fusor (as are the neutral- neutral fusions) was wrong. That these ion- neutral fusions increase towards the center until presumably the increasing ion concentrations shift the reaction probability to more favor the ion- ion fusion collisions should(?) relax the requirements for maximizing the ion/ neutral ratios in the Polywell that is required to approach B^4 scaling.
7) The graphs on page 13 show large ion, neutral and electron numbers concentrating near the cathode grid or wall at energies below several hundred electron volts. I'm guessing that this reflects some artifact as opposed to some transitional effect dependant on Debye sheaths, etc. I cannot see neutral distributions being affected by such unless there are significantly increased recombinations in those areas and conditions. Does this have any applications to the arguments about border conditions that Dr. Carlson has put forth in the past?
Keep in mind that the Polywell should maximize the ion/ neutral ratios much more than gridded fusors through both magnetic shielding, which will not only greatly decrease energy losses, but also reduce internal secondary neutral populations by ion neutralizations on internal structures such as the magrid or a material cathode grid. Actually, I don't know what the ratio of recombined neutral populations derived from free electron recombinations vs hitting the cathode or wall is, but the magnetic shielding (and virtual cathode) can only help, perhaps to a significant extent. This should also significantly decrease pollution of the system with sputtered metal ions, etc.
The other (major) advantage of the Polywell is the Wiffleball trapping factor which is claimed to increase internal ion to external ion ratios within the magrids by a factor of ~ 100-1000. Since the neutral density should be ~ equal throughout the vacuum vessel there would be no concentrating effects inside the magrid and thus the ion/ neutral ratios inside the magrids should greatly favor ion- ion fusion collisions over ion- neutral, or fast neutral- neutral collisions ( or ion- target, or neutral- target collisions in a non shielded gridded fusor).
This dominance of ions inside the machine also allows the slow ions near the Wiffleball border to anneal their transverse motions (if you accept that annealing is real) without random motion neutrals interfering.
Any comments, corrections, expansions, laughs or groans?
Dan Tibbets
